One of the biggest questions surrounding Mayor Bill de Blasio’s push for a higher income tax to pay for more prekindergarten seats in New York City is whether he could create enough seats to justify the increase.

On Tuesday, Mr. de Blasio tried to answer his skeptics, saying that up to 29,000 seats could be opened at schools and so-called community based organizations who would be under contract with the city.

“The practical elements are in place, and ready to go,” the mayor said, standing beside the schools chancellor, Carmen Fariña, during a news conference at Public School 130 in Lower Manhattan, which already offers half-day prekindergarten. “The funding is not yet, and that’s what we have to achieve.”

There was no indication, however, that Mr. de Blasio had succeeded in winning support in Albany for his proposal, which would generate money from an additional income tax on city residents earning over $500,000 a year.

His main obstacle, Gov. Andrew M. Cuomo, a fellow Democrat, has offered to pay for universal prekindergarten statewide with existing tax revenues. The governor, who is running for re-election this year, says higher taxes will drive wealthy people from New York State.

“I believe the better course is let the state pay for it since it is a statewide initiative, and the state has the funds so that we don’t have to raise taxes,” Mr. Cuomo said on Tuesday during an appearance on the Fox Business Network.

The mayor argues that the governor’s plan would not guarantee that future legislators and governors would not renege on preschool funding, as they have done in past years when state revenues dipped.

Expecting that some money will be available, the city asked its schools and private organizations to identify spaces where new prekindergarten seats could be created by September. Community-based organizations — typically local nonprofits — have identified potential seating for 20,000 students at 647 different sites, the mayor said. Additionally, principals from 280 public elementary schools have said they could provide 9,000 more seats, he said.

If just 21,000 of those seats could be used and funded, it would meet the mayor’s goal of expanding full-day prekindergarten to 53,604 children by September, on the way to a goal of 73,000 by next year. But the statistics released by the mayor on Tuesday did not say specifically where those seats would be, and the list of caveats made it clear that the city was in a race with the calendar.

The sites still need to be inspected by the city’s Education, Fire, and Health and Mental Hygiene Departments to ensure they are suitable for classrooms. And the minimum requirements for community organizations were set relatively low: They need just one year of experience with early childhood education, or absent that, they must have a leader with early childhood certification and at least two years’ experience.

School officials said they had the time, and expertise, to ensure that each provider had operational and instructional quality, by checking things like its budget, curriculum plans and staffing. They also said they would work more proactively with the city’s health department to monitor safety. In his budget address last month, Mr. Cuomo warned against programs that are “a little bit more than babysitting,” saying that quality teaching and programming were needed.

“We will also re-examine the pre-K inspections and regulations as well as construction codes for facility requirements,” Mr. Cuomo said. “Because we don’t just want to do pre-K. We want to do it great, and we will.”

A version of this article appears in print on , on Page A20 of the New York edition with the headline: City Can Add 29,000 Seats for Pre-K, Mayor Says. Order Reprints | Today’s Paper | Subscribe